#1 Explain how we know that the function f(x)=sin(x)x^2+x has a root in the interval (1,2).

#2 Find all vertical and horizontal asymptotes for h(t)=(3t+t^2) / t^2t6. Explain how you found each one using limits.

#3 Given f(x)=(3x+1) Use the definition of a derivative at a point to find f ' (a) at the value of a=5.